On the size of Satake parameters for unitary cuspidal automorphic representations for GL(4)

Let Pi be a cuspidal automorphic representation for GL(4) over a number field F. We obtain unconditional lower bounds on the number of places at which the Satake parameters are not "too large". In the case of self-dual Pi with non-trivial central character, our results imply that the set of places at which Pi is tempered has an explicit positive lower Dirichlet density. Our methods extend those of Ramakrishnan by careful analysis of the hypothetical possibilities for the structure of the Langlands conjugacy classes, as well as their behaviour under functorial lifts. We then discuss the analogous problem in GL(3). C) 2013 Elsevier Inc. All rights reserved.


Publié dans:
Journal Of Number Theory, 133, 10, 3470-3484
Année
2013
Publisher:
San Diego, Academic Press Inc Elsevier Science
ISSN:
0022-314X
Mots-clefs:
Laboratoires:




 Notice créée le 2013-10-01, modifiée le 2018-09-13


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